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Laplace transform issue

  1. Dec 9, 2011 #1
    1. The problem statement, all variables and given/known data
    f(t)=e^(t+7)


    2. Relevant equations
    £{f(t)}=∫e^(-st)f(t)dt


    3. The attempt at a solution
    so i insert my f(t) into the formula, came up with ∫e^(-st+t+7)dt
    using u substitution, u=t(-s+1)+7, du=(-s+1)dt so it follows that 1/(-s+1)∫e^(u)du=e^(u)/(-s+1)
    so I plug u back in, and should be able to find my answer from there, only I come up with an answer very different from the one in the book, which is e^(7)/(s-1)
    Can anyone help me out?

    So i figured it out, I set u=-1(t(-s+1)+7)=t(s-1)-7, and put e^-u inside the integral. turns out just making myself look at it a little longer worked out
     
    Last edited: Dec 9, 2011
  2. jcsd
  3. Dec 9, 2011 #2

    LCKurtz

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    You didn't show your work with the limits, which is where your error is. You need to either put the new u limits in your u answer or the t limits in your t answer.
     
  4. Dec 10, 2011 #3
    ok, so I figured out that last one, now i'm having difficulty with £{t^(2)e^(-2t)}. putting it into the laplace definition I come up with ∫t^(2)e^(-t(s+2))dt. I've tried integration by parts, and come up with:
    u=t^2, du=2t dt, dv=e^(-t(s+2))dt

    and that's where i get stuck, i can't seem to figure out this integration. i've plugged it into wolfram, but that turns out with v=te^(-t(s+2)), which, when plugged back into the integration by parts, leaves me with a more complicated equation, involving the negative of my original integral.
     
  5. Dec 10, 2011 #4
    You can always use integration by parts again,
     
  6. Dec 11, 2011 #5
    changed a few things around, still using integration by parts, actually integrated by parts i think three times total, if i'm remembering last night correctly, to finally end up with the right answer. thanks
     
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